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Statement -I: f: A to B is one -one and ...

Statement -I: `f: A to B` is one -one and `g: B to C` is a one-one function, then `gof : A to C` is one-one
Statement-II: If `f: A to B, g : B to A` are two functions such that gof`=I_(A)` and `fog=I_(B)`, then `f=g^(-1)`.
Statement-III: `f(x) =sec^(2)x- tan^(2)x, g(x) ="cosec"^(2)x-cot^(2)x`, then f=g. Which of the above statements is/are true:

A

only III

B

both I & III

C

both I & II

D

I, II, III

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-FUNCTIONS -EXERCISE -II
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  2. f: R^(+) to R defined by f(x) = log(e)x, x in (0,1), f(x) =2 log(e) x,...

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  3. Statement -I: f: A to B is one -one and g: B to C is a one-one functio...

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  4. Observe the following Lists: Then the match for List -1 from Lis...

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  5. If f(x) =(e^(x) + e^(-x))/2, then the inverse function of f(x) is:

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  6. If f(x) =(10^(x)-10^(-x))/(10^(x) +10^(-x)) then f^(-1)(x)=

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  7. Let f: [1/2, 1] to [-1,1] is given by f(x) =4x^(3)-3x and f^(-)(x) is ...

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  8. The domain fo f(x)=(1)/(|sinx|+sinx) is

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  9. The domain of the function: f(x) =(tan 2x)/(6 cos x + 2 sin 2x) is:

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  10. The domain of the function f(x) = sqrt("cosec"x-1) is:

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  11. If f(x)=|sinx| has an inverse if its domain is

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  12. Domain of sin^(-1) 5x is:

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  13. The doamin of sqrt(1-3x)+Cos^(-1).(3x-1)/(2) is

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  14. Domain of Cos^(-1)sqrt(3x) is

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  15. The domain of the function f(x) =sqrt(sin^(-1)x) is:

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  16. The domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) ...

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  17. The domain of sin^(-1)[(3x-1)/2] + sqrt(cos(sin x)) is:

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  18. The domain of the function: f(x) = sqrt(sin^(-1)(log(2)x)) + sin^(-...

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  19. The domain of f(x)=("cosec"^(-1)x)/([x]) is

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  20. The domain of sin^(-1)(x/2-1)+ logsqrt(x-[x]) is:

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